A Digital Proportional–Resonant Controller With Desired Tracking-Error Convergence

Proportional-resonant (PR) controllers were initially presented within a continuous-time control framework; hence, their digital implementations may be susceptible to resonant-frequency offset and modulation-signal computational delay. Consequently, engineers may need to tune the controller parameters by trial and error to design the control systems that achieve desired performance. In digital control, sinusoidal references of power converters are discrete-time sequences. Based on this, we present a digital design technique for the PR controllers and demonstrate the design process using a 13.2-kW grid-connected inverter prototype. The design ensures the sinusoidal reference's tracking-error sequence converges at the desired rate. The advised design technique's merits include: 1) The tracking-error convergence rate, phase margin, and cut-off frequency have clear mathematical relations, allowing engineers to uniquely determine the controller parameters by specifying any two indicators. 2) With the tuned controller parameters, the tracking-error sequence can converge at the desired rate. 3) The resultant controller can be partitioned into one proportional term and two resonant terms; the first two terms are construed as a standard PR controller digitally implemented via the zero-order-hold method, whereas the second resonant term guarantees the tracking-error sequence converging in the desired manner. A case study results confirm the digital PR controller's efficacy.